Ab initio theoretical studies on U3+ and on the structure and spectroscopy of U3+ substitutional defects in Cs2NaYCl6, 5f26d1 manifold

Ab initio theoretical studies on U

and on the structure

and spectroscopy of U

substitutional defects in Cs

NaYCl

, 5 f

6 d

manifold

Luis Seijo^a)and Zoila Barandiara´n

Departamento de Quı´mica, C-XIV, and Instituto Universitario de Ciencia de Materiales Nicola´s Cabrera, Universidad Auto´noma de Madrid, 28049 Madrid, Spain

共Received 10 December 2002; accepted 3 January 2003兲

In this paper we present the results of spin–orbit relativistic ab initio model potential embedded cluster calculations of the 5 f²6d¹ excited manifold of (UCl₆)^3⫺ embedded in a reliable representation of the Cs₂NaYCl₆ elpasolite host. They are aimed at interpreting the 5 f³→5 f²6d¹ absorption bands reported by Karbowiak et al.关J. Chem. Phys. 108, 10181 共1998兲.兴 An excellent agreement is found between the calculated energies of the absorption transitions from the ground state 5 f³1⌫8u(⁴I_9/2) and the experimental data, which supports a detailed interpretation of the electronic nature of the absorption spectrum in the energy region 14 000–23 000 cm^⫺1. In particular, the three unidentified electronic origins that had been experimentally detected are now assigned, and the observed bands are interpreted as having multiple electronic origins. From the structural point of view, the excited states of the 5 f²6d¹manifold are classified in two sets of main configuration 5 f²6d(t_2g)¹ and 5 f²6d(e_g)¹ with bond distances R_e 关5 f²6d(t_2g)¹兴⬍Re关5 f³兴

⬍Re关5 f²6d(e_g)¹兴. The energies of the 5 f²6d¹ manifold of free U^3⫹ have also been calculated;

experimental data on them are not available in the literature to the best of our knowledge. These results contribute to show that wave function based ab initio methods can provide useful structural and spectroscopic information, complementary to the experimental data, in studies on actinide ion impurities doping ionic hosts, where large manifolds of 5d^n⫺16d¹ excited states are involved.

© 2003 American Institute of Physics. 关DOI: 10.1063/1.1555120兴

I. INTRODUCTION

Actinide impurity ions in ionic hosts have large mani- folds of excited states of the 5 f^n⫺16d¹ configuration which are interesting from basic and applied points of view. In the free ions, these states are much higher in energy than those of the 5 fⁿ configuration, but the energy required for a 5 f

→6d excitation is very much reduced in crystals and is strongly dependent on the crystal host.^1,2This excitation en- ergy is lower than the 4 f→5d excitation in lanthanide ion doped crystals, where 5d→4 f broad emission bands are in- volved in applications as phosphors, scintillators, and visible-UV solid-state laser materials.^3–5The f^n⫺1d¹ energy levels of f-element impurity ions may be involved in photon cascade emission processes⁶and act as intermediate states in electronic Raman scattering⁷ and in photon upconversion processes.^8,9Also, the relative low energy of the 5 f^n⫺16d¹ levels of the actinide impurity ions makes the analysis of the 5 f→5 f spectra more complex.¹⁰ 5 f→6d absorption and 6d→5 f emission transitions have been observed in actinide ion impurities共e.g., Pa^4⫹:Cs₂ZrCl₆,^11,12U^3⫹:Cs₂NaYCl₆,¹⁰ or Cm^3⫹:Cs₂NaYCl₆,¹³兲 but they are often not well under- stood and detailed assignments have only been made in the 5 f¹→6d¹ case.¹²

In these circumstances, wave function-based ab initio methods of quantum chemistry are indicated, provided that they include all the relevant interactions: all the bonding in-

teractions within the cluster formed by the impurity and its first coordination shell, including electron correlation effects and scalar and spin–orbit coupling relativistic effects, and the embedding interactions between the cluster and the rest of the host. In this line, ab initio calculations of the 5 fⁿ manifold and of some charge transfer states of actinyl ions have been shown to be instrumental in the understanding of their electronic structure and spectra in solid state and in solution.^{14 –17}Also, spin–orbit relativistic ab initio model po- tential 共AIMP兲 embedded cluster calculations¹⁸ have been shown to produce reliable results of the small 6d¹ manifold of Pa^4⫹ in Cs₂ZrCl₆, providing a new interpretation of the absorption spectrum,¹⁹and of the large 5 f¹6d¹ manifold of U^4⫹ in Cs₂ZrCl₆, suggesting its involvement in the mecha- nism of green to blue light upconversion.²⁰

In this paper, we present the results of AIMP theoretical calculations of the large 5 f²6d¹ manifold of U^3⫹ in the Cs₂NaYCl₆ host. They are aimed at interpreting the rich 5 f³→5 f²6d¹ absorption bands that have been reported by Karbowiak et al.¹⁰ and lack a detailed assignment. The re- sults on the same manifold of free U^3⫹ ion are also pre- sented; they are an important reference for the interpretation of the levels of the U^3⫹impurities in solid hosts and they are not available in the literature.

II. DETAILS OF THE CALCULATIONS

The interest of this paper is focused on a large manifold of electronic states of U^3⫹-doped Cs₂NaYCl₆that are local- ized on the U^3⫹ impurities. These impurities substitute for

a兲Electronic mail: [email protected]

5335

0021-9606/2003/118(12)/5335/12/$20.00 © 2003 American Institute of Physics

some of the Y^3⫹ions in an O_h site with a first coordination shell of six Cl^⫺ions.¹⁰These local states depend, mainly, on all the electronic interactions within U^3⫹and on the bonding interactions between U^3⫹ and the six Cl^⫺ ions, and, to a lesser extent, on the interactions between the (UCl₆)^3⫺clus- ter and the rest of the host. In consequence, a method is needed which reliably considers:共i兲 the scalar and spin–orbit coupling relativistic effects of uranium, 共ii兲 a significant amount of electron correlation effects in a large number of states of the (UCl₆)^3⫺ cluster, and 共iii兲 the classical and quantum embedding effects brought about by the Cs₂NaYCl₆ ionic host into the (UCl₆)^3⫺cluster. We have used the AIMP embedding method²¹ for the third purpose, together with the Wood–Boring²²-based effective core potential two- component relativistic Hamiltonian WB-AIMP²³for the first one. The simultaneous treatment of electron correlation and spin–orbit coupling, which is very demanding here, has been handled by means of spin–orbit multireference configuration interaction calculations 共MRCI兲 using the spin-free-state- shifted Hamiltonian,²⁴ which allows to transfer electron cor- relation effects from calculations with a spin-free Hamil- tonian to calculations with a spin–orbit Hamiltonian.

Bonding interactions and nondynamic correlation effects have been taken into account in complete active space self- consistent field calculations, CASSCF,²⁵and multistate com- plete active space second-order perturbation theory, MS-CASPT2,^{26 –29}has been used in order to handle the ad- ditional nondynamic correlation effects in the large number of (UCl₆)^3⫺ excited states involved.

A. Embedded cluster Hamiltonian

The AIMP Hamiltonian that corresponds to the previous description of the method is fully detailed in Ref. 18. We summarize it here. It is the following valence only, spin–

orbit relativistic Hamiltonian of the (UCl₆)^3⫺cluster embed- ded in a Cs₂NaYCl₆ lattice:

Hˆ

sfss AIMP⫽

兺

N_val^clus

再

^兺

冋

⫹hˆ_␮^SO共i兲

册

^兺

冎

^兺

^兺

⫹_␮苸clus^N

兺

clus

␯(⬎␮)苸clus

兺

N_nuc^clus

Z_␮^effZ_␯^eff R_␮␯ ⫹

兺

P

␦␥兩⌽SF,P ␥典具⌽SF,P ␥兩.

共1兲 In Eq. 共1兲, the indices i and j refer to the Nval

clus valence electrons of the cluster, ␮ ^and ␯ refer to the N_nuc^clus nuclei 共atoms兲 of the (UCl6)^3⫺ cluster, each of them having N_␮^core core electrons and an effective nuclear charge Z_␮^eff⫽Z_␮

⫺N_␮^core. The ␰ index refers to the N_ion^host ions of the Cs₂NaYCl₆ embedding host, i.e., all the ions in the doped material except the U^3⫹ impurity and its first coordination shell of six Cl^⫺ions.

Vˆ

␮⫺core

AIMP (i) is the one-electron spin-free relativistic ab initio model potential,³⁰ which represents the effects of the core electrons of atom ␮ 共an effective core potential兲 plus

the scalar Darwin and mass–velocity atomic potentials of Cowan and Griffin 共which are variationally stable兲³¹ acting on the valence electrons. It reads

Vˆ

␮⫺core AIMP 共i兲⫽ 1

r_␮i

兺

兺

兺

⫻A␮j,k具␹k␮兩⫹c苸␮⫺core

兺

The first term in the right-hand side of Eq.共2兲 is the core Coulomb model potential, which is produced by least- squares fitting to the true core Coulomb potential of atom

␮^.32 The second term is the core exchange, plus Darwin, plus mass–velocity model potential, which is produced by the spectral representation of the true operators in the space defined by the one-center basis set兵^兩␹j␮典其^;32 this basis set is chosen to be the set of Gaussian primitive functions used in the embedded cluster calculation that are centered on atom

␮. The third term is the core shifting operator of Huzinaga and Cantu³³ that prevents the valence orbitals from collaps- ing onto the core orbitals.

hˆ_␮^SO(i) is the one-electron spin–orbit model potential.²³ It results from the true spin–orbit operator of Wood and Boring,²²after using: 共a兲 a suitable analytical representation of the radial components of the Wood–Boring spin–orbit operator, produced by least-squares fitting, and 共b兲 an angu- lar projection of the atomic 艎ˆ^␮sˆ operator according to Pitzer and Winter.³⁴It reads

hˆ_␮^SO共i兲⫽␭_␮nᐉ苸␮⫺val

兺

兺

r_␮i²

⫻Oˆ_ᐉ^␮艎ˆ^␮sˆOˆ

ᐉ␮, 共3兲

where the angular projection operator Oˆ

ᐉ␮is defined in terms of the spherical harmonics centered on␮

Oˆ

ᐉ␮⫽m

兺

⫹ᐉ

兩Y_ᐉm^␮ 典具^Y_ᐉm^␮ 兩. 共4兲

Since the Wood–Boring spin–orbit coupling operator leads to systematic overestimations of the atomic spin–orbit cou- pling constants of around 10%,²³we use a spin–orbit atomic scaling factor ␭_␮ in Eq.共3兲. In this paper we use ␭U⫽0.9, which has been found to be good for the 5 f² manifold of U^4⫹-doped Cs₂ZrCl₆.²⁰

Vˆ

␰⫺ion emb-AIMP

(i) is the contribution of the host ion␰ ^{to the} one-electron embedding model potential.²¹ It reads

Vˆ

␰⫺ion

emb-AIMP共i兲⫽⫺Q_␰ r_␰i⫹ 1

r_␰i

兺

⫹

兺

兺

⫹_{c苸␰⫺ion}

兺

This single-ion embedding model potential is isomorphous with the core model potential, Eq. 共2兲, except for the pres- ence of the term⫺Q_␰/r_␰i, which represents the long-range Coulomb共Madelung兲 potential created by a point charge Q_␰ 共the ionic charge.兲 The next two terms of this model potential are approximations, respectively, to the short-range Coulomb potential of the full ion 共which is defined as the Coulomb potential of the full ion minus the long-range Coulomb po- tential兲 and to the full ion exchange operator. They are pro- duced like the corresponding terms in Eq. 共2兲. The last term in Eq.共5兲 is the full ion shifting operator, which prevents the cluster wave functions from collapsing onto this particular lattice ion.³³

The last term in Eq. 共1兲 is a spin-free-state-shifting operator.²⁴ Based on the ideas of Teichteil et al.,³⁵ it is a practical means to transfer large amounts of electron corre- lation effects from a sophisticated calculation with a spin- free Hamiltonian共e.g., a CI calculation within a very large G configuration space兲 to a much simpler calculation with a spin–orbit Hamiltonian 共e.g., a spin–orbit CI calculation within a small P configuration space.兲 In it, 兩⌽SF,P ␥典 ^{is the} wave function of state␥ that corresponds to the small space P and to the spin-free Hamiltonian. The shifting coefficient

␦␥ is calculated using the energies of state␥ and of a refer- ence state 0 共usually the ground state,兲 corresponding to the spin-free Hamiltonian, as calculated within a small configu- ration spaceP: E0Pand E_␥^P, and within a large configuration space G: E0Gand E_␥^G

␦␥⫽关E_␥^G⫺E0G兴⫺关E_␥^P⫺E0P兴. 共6兲 N_SF^P is the number of states of the spin-free Hamiltonian included in the shifting operator. Although its choice is arbi- trary, the projection of the final wave functions of the spin–

orbit Hamiltonian on the space spanned by the N_SF^P wave functions兩⌽SF,P ␥典 can be used for a systematic evaluation of N_SF^P .³⁶Our choice here makes the projection of all the states of interest to be larger than 99.95%.

B. Details of the calculations

In addition to the 5 f²6d¹ manifold of the (UCl₆)^3⫺ cluster embedded in Cs₂NaYCl₆, we also calculated the par- ent excited states of the U^3⫹ free ion, which are useful for interpretation. In both systems, the calculations were done in two steps: In a first step, in which all the relevant electron correlation effects are the main focus of attention, the spin- free Hamiltonian was used

Hˆ

spin-free AIMP ⫽Hˆsfss

AIMP⫺

兺

P

␦␥兩⌽_SF,␥^P 典具⌽_SF,␥^P 兩

⫺i

兺

␮苸clus

兺

N_nuc^clus

hˆ_␮^SO共i兲, 共7兲

which is formally identical to a nonrelativistic Hamiltonian;

we performed this step with the MOLCAS-5 package.³⁷ In a second step, in which the main interest is shifted towards spin–orbit coupling effects, the spin–orbit Hamiltonian

Hˆ

sfss

AIMP 关Eq. 共1兲兴 was used; we performed this step with a modified version of theCOLUMBUSpackage.³⁸

The关Xe,4f 兴 core AIMPs of neutral actinoids were found to be appropriate for the 5 fⁿ and 5 f^n⫺16d¹ manifolds of actinide ions;³⁹accordingly, we used the关Xe,4f 兴 core AIMP 关Eq. 共2兲兴 of neutral U (5 f³6d¹7s²)⁵K.^39,40 We used a (14s10p12d9 f 3g)/关6s4p5d4 f 2g兴 Gaussian valence basis set for U 共see Sec. II C兲. For Cl, we used the 关Ne兴 core AIMP³⁰ together with a valence basis set (7s7 p1d) con- tracted as 关3s4p1d兴, which resulted from the minimal (7s6 p) basis set of Ref. 30 upon split, and addition of one p diffuse function for anions⁴¹ and one d polarization function.⁴² The d polarization functions of Cl and the g po- larization functions of U were formally removed in the spin–

orbit calculations; note, however, that their effects on the spin–orbit states are taken into account by means of the spin- free-state-shifting operator.

We used the Cs₂NaYCl₆AIMP embedding potential of Ref. 43, which was produced in self-consistent embedded ions calculations; it is made of a sum of 482 single-ion AIMPs 关Eq. 共5兲兴 of the Cs^⫹, Na^⫹, Y^3⫹, and Cl^⫺ ions sur- rounding the cluster, plus 2696 extra point charges that allow for a correct description of the long-range Madelung poten- tial; all of the single-ion AIMPs and point-charges are lo- cated at experimental sites 关Cs2NaYCl₆(O_h⁵-F_m3m), a⫽10.7396 Å, xCl⫽0.243 93.]⁴⁴

The two-step calculations on free U^3⫹ion were done as follows: We performed spin-free Hamiltonian CASSCF cal- culations共with an active space defined by all possible distri- butions of 3 electrons in 13 active atomic orbitals 5 f , 6d, and 7s) in the average of all doublets from 1²H to 2²H and all quartets from ⁴K to 2⁴G of the 5 f² 6d¹ manifold, fol- lowed by MS-CASPT2 calculations in which 11 electrons were correlated共those in the active orbitals and in the 6s and 6 p closed-shells兲. In the second step, we performed spin–

orbit Hamiltonian spin-free-state-shifted MRCI共S兲 calcula- tions in which only single excitations from the 5 f and 6d atomic orbitals to the virtual space were allowed from the CAS multireference 共the P space;兲 the atomic orbitals opti- mized in the SA-CASSCF calculations were used here. This kind of spin–orbit CI calculations has been found to be suf- ficient for a good description of spin–orbit splittings.³⁶The E₀^G and E_␥^G energies in the shifting coefficients␦␥ 关Eq. 共6兲兴 were calculated with the MS-CASPT2 results and they are shown in Table I.

In the (UCl₆)^3⫺ octahedral cluster embedded in Cs₂NaYCl₆, we first performed spin-free Hamiltonian state average complete active space self-consistent field calcula- tions, SA-CASSCF,²⁵with 3 electrons in 13 active molecular orbitals with main character U 5 f , 6d, and 7s (a_2u, t_2u, t_1u, t_2g, e_g, and a_1g) which we will call SA-CASSCF 关5 f ,6d,7s兴.³ Four sets of molecular orbitals were produced for each nuclear configuration, each in a separated SA- CASSCF calculation: 共a兲 MOs that minimize the average energy of all ⁴A_1g, ⁴A_2g, and ⁴E_g states up to 3 ⁴A_1g, 5

4A_2g, and 8⁴E_g, all of them having a main configuration U 5 f²6d¹ 关either 5 f²6d(t_2g)¹ or 5 f²6d(e_g)¹,] the next state being of main character U 5 f²7s¹; 共b兲 MOs that minimize the average energy of all⁴T_1g and⁴T_2gstates up to 13⁴T_1g

and 12 ⁴T_2g, which includes U 5 f²6d(t_2g)¹ and U 5 f²6d(e_g)¹ states; 共c兲 MOs that minimize the average en- ergy of all²A_1g,²A_2g, and²E_gstates up to 3²A_1g, 2²A_2g, and 5 ²E_g 共included in an energy window of around 12 000 cm^⫺1, the next state of these irreducible representations be- ing 3000 cm^⫺1 above兲 and 共d兲 MOs that minimize the aver- age energy of all ²T_1g and²T_2g states up to 7 ²T_1g and 8

2T_2g共included in an energy window of around 13 000 cm^⫺1, the next state of these irreducible representations being 1000 cm^⫺1 above兲. The CAS-CI energies of all the states of the

given irreducible representations have been calculated using their corresponding MOs. All this produces structural and spectroscopic results at a CASSCF level, but it also produces the necessary ingredients for MS-CASPT2 calculations.^{26 –29} The MS-CASPT2 calculations performed include dynamic correlation of 11 electrons occupying the active MOs and the MOs with main character U 6s and U 6 p, plus 48 electrons occupying MOs with main ligand character Cl 3s and Cl 3 p.

These calculations are labeled MS-CASPT2共Cl48,U11兲. All these methodological choices are justified in Sec. II C. Fi-

TABLE I. Energy levels of the 5 f²6d¹configuration of free U^3⫹. Results of MS-CASPT2 calculations (6s, 6 p, 5 f , and 6d electrons are correlated兲 with the spin-free Hamiltonian关Eq. 共7兲兴 and spin-free state shifted MRCI共S兲 calculations with the spin–orbit Hamiltonian 关Eq. 共1兲兴 are presented. The values of the spin-free state shifting parameters␦␥关Eq. 共6兲兴 used in the spin–orbit MRCI共S兲 calculation and the correspondence between free-ion and Ohcluster levels are also presented. All energies are in cm^⫺1. Note that all the states are gerade. Total共valence only兲 energies of the term⁴K and the lowest level J⫽11/2 are

⫺217.397 590 and ⫺217.449 429 a.u., respectively.

Spin-free Hamiltonian关Eq. 共7兲兴

Term Energy^a ␦␥关Eq. 共6兲兴 Related Ohspin-free states

4A1g

4A2g

4Eg

4T1g 4T2g

2A1g 2A2g

2Eg 2T1g

2T2g

1²H ⫺3 340 ⫺1 210 0 0 1 2 1

4K 0 0 0 1 1 2 2

1²F 700 ⫺3 340 0 1 0 1 1

1⁴G 1 080 0 1 0 1 1 1

4I 1 100 0 1 1 1 1 2

2I 1 550 440 1 1 1 1 2

1⁴H 2 560 ⫺550 0 0 1 2 1

1²D 4 160 ⫺3 750 0 0 1 0 1

4P 4 230 ⫺2 370 0 0 0 1 0

2P 4 410 ⫺5 850 0 0 0 1 0

2⁴H 4 830 ⫺4 100 0 0 1 2 1

1²G 5 720 ⫺4 180 1 0 1 1 1

1⁴F 5 970 ⫺4 250 0 1 0 1 1

2²H 6 340 ⫺1 890 0 0 1 2 1

4D 6 950 ⫺5 030 0 0 1 0 1

2²F 7 150 ⫺4 890 0 1 0 1 1

2²G 7 540 ⫺4 320 1 0 1 1 1

2⁴G 7 850 ⫺3 650 1 0 1 1 1

2K 9 640 ⫺2 050 0 1 1 2 2

2⁴F 10 490 ⫺4 920 0 1 0 1 1

2²D 10 700 ⫺4 840 0 0 1 0 1

Spin–orbit Hamiltonian关Eq. 共1兲兴 Level^b Energy^c Related O¯_hspin–orbit states

⌫6g ⌫7g ⌫8g

11/2 (⁴K 67,⁴I 25兲 0 1 1 2

9/2 (⁴I 50, 1²H 34兲 1 420 1 0 2

5/2共1⁴G 44, 1²F 40兲 2 040 0 1 1

7/2共1⁴H 61, 1²G 14兲 4 230 1 1 1

9/2共1²H 51,⁴I 31兲 5 320 1 0 2

11/2共1²H 49,⁴K 21兲 5 680 1 1 2

13/2 (⁴K 90,²I 9兲 6 440 1 2 2

1/2 (²P 55,⁴D 22兲 6 480 1 0 0

7/2共2⁴H 44, 1⁴G 29兲 7 030 1 1 1

7/2共2⁴H 35, 1⁴G 33兲 7 850 1 1 1

11/2 (⁴I 84, 2²H 7兲 8 000 1 1 2

5/2共1⁴G 40, 1²D 30兲 9 380 0 1 1

9/2共1⁴H 81, 1⁴G 7兲 9 570 1 0 2

3/2共1⁴P 38,²P 24兲 10 700 0 0 1

9/2共2⁴H 36, 1⁴G 17兲 11 190 1 0 2

5/2共2⁴G 27, 1⁴F 27兲 11 300 0 1 1

3/2共1⁴F 77, 1²D 10兲 11 670 0 0 1

aRelative to 5 f²6d¹⫺⁴K, which is 30 850 cm^⫺1above the 5 f³⫺⁴I ground term.

bThe values of J are indicated, together with the leading term characters, in percentage.

cRelative to lowest state of the 5 f²6d¹configuration, J⫽11/2 (⁴K), which is 27 940 cm^⫺1above the 5 f³J⫽9/2 (⁴I) ground state.

nally, we performed spin–orbit Hamiltonian spin-free-state- shifted MRCI共S兲 calculations. The CI space was defined by the CAS multireference plus all single excitations from the MOs with main character U 5 f and U 6d. Here, the CASSCF MOs and the shifting coefficients␦␥corresponding to the MS-CASPT2共Cl48,U11兲 results were used. The spin–

orbit potentials 关Eq. 共3兲兴 were taken from Refs. 40 共U兲 and 45共Cl兲.

C. Active space, basis set, and dynamic correlation In this section, we present the results of a numerical study addressed to establish methodological conditions which are appropriate for practical studies of 5 f³ and 5 f²6d¹ manifolds of (UCl₆)^3⫺, meaning that they fulfill conditions of acceptable precision at a reasonable computa- tional cost. We consider here the active space, the basis set of U, and the dynamic correlation. We expect the conclusions of this section to be transferable to the 5 fⁿand 5 f^n⫺16d¹mani- folds of other actinide ion halides.

SA-CASSCF calculations in Cs₂NaYCl₆: (UCl₆)^3⫺ with an active space resulting from distributing 3 electrons in 12 active molecular orbitals with main character U 5 f and 6d, SA-CASSCF 关5 f ,6d兴³, lead to results of U–Cl bond distances, breathing mode frequencies, minimum-to- minimum energy differences, and vertical共Franck–Condon兲 energy differences, essentially coincident with those of SA- CASSCF 关5 f ,6d,7s兴³ calculations. However, all the CASPT2 calculations with the SA-CASSCF关5 f ,6d兴³ refer- ence lead to a number of intruder states that contaminate the results of several excited states. The contaminated states were different for different basis sets and for different choices of zero-order Hamiltonian, but there were always some intruder states. They were fully removed after includ- ing in the CAS space the MO with main character U 7s, that is, by using a SA-CASSCF 关5 f ,6d,7s兴³ reference. Accord- ingly, the results presented in this paper correspond to a 关5 f ,6d,7s兴³ complete active space of (UCl₆)^3⫺. We expect this CAS to be also necessary for other 3⫹ actinide ions. We may mention that including the U 7s orbital in the active space was not found to be necessary for U^4⫹hexachloride,²⁰ where the energy difference between 6d and 7s is larger.

The 关6s5p6d4 f 兴 contraction of the (14s10p12d9 f ) primitive Gaussian basis set corresponding to the 关Xe,4f 兴 core was recommended for molecules containing actinide elements.³⁹ In the case of 5 fⁿ and 5 f^n⫺16d¹ configurations of multiply ionized actinides like U^3⫹, where the 7s orbital is empty and 6d orbitals more compact than in neutral atoms are present, smaller contractions of the basis set might be useful. The results of a systematic study on the basis set contraction are shown in Table II, where the effects of addi- tional g polarization functions are also shown共by addition of the outermost primitives to a 3g contracted function pro- duced by maximum radial overlap with the 5 f orbital of U兲.

In the table, we present SA-CASSCF 关5 f ,6d,7s兴³ calcula- tions as well as two sets of MS-CASPT2 calculations: one which includes dynamic correlation of the 3 electrons in the active MOs plus the 36 electrons in MOs with main character Cl 3 p 共Cl36,U3兲, and a second one with additional dynamic correlation from the U 6s and 6 p, and Cl 3s electrons

共Cl48,U11兲, so that the effects of dynamic correlation can also be shown. We calculated the following states of the spin-free Hamiltonian of Cs₂NaYCl₆: (UCl₆)^3⫺ at r共U–Cl兲 ⫽ 2.752 Å: 5 f³⫺1⁴E_u(⁴I), 5 f³⫺1⁴A_2u(⁴I), 5 f³

⫺2⁴A_1u(⁴S), 5 f²6d(t_2g)¹⫺1⁴A_2g, and 5 f²6d(e_g)¹

⫺4⁴A_2g. With the first two, we can monitor the effects on two states related to the same atomic term, that is, the effects on the 5 f crystal field splitting; the third one allows one to monitor the effects on a 5 f→5 f transition connecting two states related to different atomic terms; the fourth state gives the effects on a 5 f→6d transition, and, finally, the fifth state allows one to know the effects on the 6d crystal-field split- ting (t_2g⫺eg), by comparison with the fourth.

In Table II we observe very small effects of addition of one f primitive to the 关6s5p6d4 f 兴 set, as well as of reduc- tion of one p and d primitives, whatever the level of calcu- lation is. The only significant effect of the reduction of one s primitive is a small increase of almost 500 cm^⫺1 in the 5 f

→6d transitions; even though this is acceptable, we take the 关6s4p5d4 f 兴 set as a basis for further experimentation with g functions. These g functions are insignificant at the CASSCF level of calculation, with a maximum effect of 100 cm^⫺1. However, they become relevant for dynamic correlation: in effect, at the MS-CASPT2共Cl36,U3兲 level they increase by 1500 cm^⫺1 the 5 f→6d(t2g) transition and lower by ap- proximately 1300 cm^⫺1 the 6d crystal field splitting;

at the 共Cl48,U11兲 level these increments become 4500 and 1200 cm^⫺1, approximately. The (14s10p12d9 f 3g)/

关6s4p5d4 f 2g兴 results do not essentially change upon addi- tion of one extra g functions; this seems to be a good choice of basis set. Finally, by comparing共Cl36,U3兲 and 共Cl48,U11兲 results, its is clear that dynamic correlation from Cl 3s and U 6s and 6 p orbitals should not be neglected for the states under study.

III. RESULTS A. U^3¿

The calculated levels of the 5 f²6d¹ configuration of U^3⫹ are shown in Fig. 1 and Table I, where the analysis in terms of SL functions is included. Experimental data on these levels are not available in the literature to the best of our knowledge. Although the lowest term of the spin-free Hamiltonian is ²H, which is 3340 cm^⫺1 more stable than

4K, the large spin–orbit coupling stabilizes the spin quartet states and the four lowest states show main contributions from ⁴K, ⁴I, 1⁴G, and 1⁴H. These lowest states have J

⫽11/2, 9/2, 5/2, and 7/2, respectively. The next two states, with J⫽9/2 and 11/2, show dominant spin doublet character (1²H) and the next one is mainly the J⫽13/2 spin–orbit component of ⁴K. The first state, J⫽11/2 (⁴K), is 27 940 cm^⫺1 above the 5 f³ J⫽9/2 (⁴I) ground state, and the next states with dominant quartet character are separated by 1420, 620, 2190, and 2210 cm^⫺1. As we will comment below, the absorption spectrum of U^3⫹-doped Cs₂NaYCl₆ is related to these states according to our interpretation.

B. Cs₂NaYCl₆:„UCl₆…^3À

First, we show in Table III a summary of the results of the spin-free Hamiltonian calculations 关Eq. 共7兲兴 on the (UCl₆)^3⫺ cluster embedded in Cs₂NaYCl₆. These calcula- tions are a first and necessary step in the procedure leading to

the final results which include electron correlation and spin–

orbit coupling effects, but they already provide useful struc- tural information because it does not change with spin–orbit coupling, as we will see 共Table IV兲.

At the CASSCF level 共where all the embedding and

TABLE II. Basis set and dynamic correlation effects on selected transitions of Cs2NaYCl6:(UCl6)^3⫺ with r共U–Cl兲⫽2.752 Å. The complete active space of all calculations corresponds to the distribution of 3 electrons in the 13 MOs with main character U 5 f , 6d, and 7s. All energies in cm^⫺1.

Basis set 5 f³⫺1⁴Eu(⁴I)→ SA-CASSCF MS-CASPT2 MS-CASPT2

contraction 共Cl36,U3兲 共Cl48,U11兲

Primitive set (14s10p12d9 f )

关6s5p6d4 f 兴 →1⁴A2u(⁴I)^a ⫺512 356 835

→2⁴A1u(⁴S)^b 8 686 7 877 6 754

→1⁴A_2g^c 12 470 9 070 11 110

→4⁴A_2g^d 34 850 29 400 27 730

1⁴A_2g→4⁴A_2g^e 22 380 20 330 16 620

关6s5p6d5 f 兴 →1⁴A2u ⫺512 360 838

→2⁴A1u 8 684 7 872 6 746

→1⁴A2g 12 460 9 120 11 170

→4⁴A2g 34 860 29 430 27 770

1⁴A2g→4⁴A2g 22 400 20 310 16 600

关6s4p6d4 f 兴 →1⁴A2u ⫺510 312 820

→2⁴A1u 8 697 7 982 6 885

→1⁴A2g 12 640 9 200 11 230

→4⁴A2g 35 040 29 570 27 910

1⁴A2g→4⁴A2g 22 400 20 370 16 680

关6s4p5d4 f 兴 →1⁴A2u ⫺509 315 833

→2⁴A1u 8 717 8 012 6 962

→1⁴A2g 12 690 9 360 11 430

→4⁴A2g 35 100 29 790 28 280

1⁴A2g→4⁴A2g 22 410 20 430 16 850

关5s4p5d4 f 兴 →1⁴A2u ⫺508 297 832

→2⁴A1u 8 734 8 035 7 010

→1⁴A2g 13 150 9 820 11 830

→4⁴A2g 35 600 30 320 28 750

1⁴A2g→4⁴A2g 22 450 20 500 16 920

Primitive set (14s10p12d9 f 3g)

关6s4p5d4 f 1g兴 →1⁴A2u ⫺595 332 953

→2⁴A_1u 8 735 7 411 6 288

→1⁴A_2g 12 680 10 850 15 970

→4⁴A_2g 35 110 29 980 31 640

1⁴A2g→4⁴A2g 22 430 19 130 15 670

关6s4p5d4 f 2g兴 →1⁴A2u ⫺591 403 1 069

→2⁴A1u 8 746 7 460 6 319

→1⁴A2g 12 610 10 480 15 550

→4⁴A2g 35 050 29 530 31 170

1⁴A2g→4⁴A2g 22 440 19 050 15 620

关6s4p5d4 f 3g兴 →1⁴A2u ⫺594 381 1 108

→2⁴A1u 8 753 7 438 6 300

→1⁴A2g 12 620 10 570 15 800

→4⁴A2g 35 060 29 530 31 330

1⁴A2g→4⁴A2g 22 440 18 960 15 530

a5 f→5 f intraterm transition.

b5 f→5 f interterm transition.

c5 f→6d(t2g).

d5 f→6d(eg).

e5 f²6d(t2g)¹⫺1⁴A2g→5 f²6d(eg)¹⫺4⁴A2g, which is a measure of the 6d crystal field splitting, and it is very approximately the crystal field theory parameter 10Dq.